Let W be a finite word on a two symbol alphabet {0,1}; let us say that W is maximal if it is the last item in the list of all its cyclic permutation (ordered lexicographically).

So, for instance: {0,1} are the maximal words of length 1; {00, 10, 11} are the maximal words of length 2; {000, 100, 110, 111} are the maximal words of length 3; {0000, 1000, 1010, 1100, 1110, 1111} are the maximal words of length 4; {00000, 10000, 10100, 11000, 11010, 11100, 11110, 11111} are the maximal words of length 5; ... und so weiter.

Let k(n):= number of maximsl words of length n

Is there some formula for k(n)?

Let W be a finite word on a two symbol alphabet {0,1}; let us say that W is maximal if it is the last item in the list of all its cyclic permutation (ordered lexicographically).

So, for instance: {0,1} are the maximal words of length 1; {00, 10, 11} are the maximal words of length 2; {000, 100, 110, 111} are the maximal words of length 3; {0000, 1000, 1010, 1100, 1110, 1111} are the maximal words of length 4; {00000, 10000, 10100, 11000, 11010, 11100, 11110, 11111} are the maximal words of length 5; ... und so weiter.

Let k(n):= number of maximal words of length n

Is there some formula for k(n)?

Let W be a finite word on a two symbol alphabet {0,1}; let us say that W is maximal if it is the last item in the list of all its cyclic permutation (ordered lexicographically).

So, for instance: {0,1} are the maximal words of length 1; {00, 10, 11} are the maximal words of length 2; {000, 100, 110, 111} are the maximal words of length 3; {0000, 1000, 1010, 1100, 1110, 1111} are the maximal words of length 4; {00000, 10000, 10100, 11000, 11010, 11100, 11110, 11111} are the maximal words of length 5; ... und so weiter.

Let k(n):= number of minimal words of length n

Is there some formula for k(n)?

Let W be a finite word on a two symbol alphabet {0,1}; let us say that W is maximal if it is the last item in the list of all its cyclic permutation (ordered lexicographically).

So, for instance: {0,1} are the maximal words of length 1; {00, 10, 11} are the maximal words of length 2; {000, 100, 110, 111} are the maximal words of length 3; {0000, 1000, 1010, 1100, 1110, 1111} are the maximal words of length 4; {00000, 10000, 10100, 11000, 11010, 11100, 11110, 11111} are the maximal words of length 5; ... und so weiter.

Let k(n):= number of maximsl words of length n

Is there some formula for k(n)?